How do you simplify (2 1/3 )/(1 2/5)?

Feb 12, 2017

See the entire simplification process below:

Explanation:

First, we must convert these mixed fractions into improper fractions by multiplying the integer portion by the correct form of $1$ and then adding the result to the fraction:

$\frac{2 \frac{1}{3}}{1 \frac{2}{5}} = \frac{\left(\frac{3}{3} \times 2\right) + \frac{1}{3}}{\left(\frac{5}{5} \times 1\right) + \frac{2}{5}} = \frac{\frac{6}{3} + \frac{1}{3}}{\frac{5}{5} + \frac{2}{5}} = \frac{\frac{7}{3}}{\frac{7}{5}}$

We can now divide this expression using this rule for dividing fractions:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

Substituting the values from our previous calculation gives:

$\frac{\frac{\textcolor{red}{7}}{\textcolor{b l u e}{3}}}{\frac{\textcolor{g r e e n}{7}}{\textcolor{p u r p \le}{5}}} = \frac{\textcolor{red}{7} \times \textcolor{p u r p \le}{5}}{\textcolor{b l u e}{3} \times \textcolor{g r e e n}{7}} = \frac{\cancel{\textcolor{red}{7}} \times \textcolor{p u r p \le}{5}}{\textcolor{b l u e}{3} \times \cancel{\textcolor{g r e e n}{7}}} = \frac{5}{3}$

Or

$\frac{5}{3} = \frac{3 + 2}{3} = \frac{3}{3} + \frac{2}{3} = 1 + \frac{2}{3} = 1 \frac{2}{3}$